EGEE 430/ME 430 Introduction To Combustion Fall 2015 Assignm

EGEE 430/ME 430 Introduction to Combustion Fall 2015 Assignment #6 Chemical Kinetics

Using the provided combustion mechanisms and data, analyze chemical kinetics related to hydrocarbon combustion and NOx formation through theoretical calculations and computational simulations. The tasks include determining the units of rate coefficients, deriving rate expressions, modeling reaction mechanisms, and simulating shock-induced combustion processes with detailed chemical mechanisms. Specific focus is placed on reaction order, rate constants, species concentration evolutions, and the effects of water vapor on shock wave chemistry in combustion systems.

Paper For Above instruction

Understanding chemical kinetics in combustion processes is fundamental to advancing the efficiency and environmental compatibility of energy conversion systems. This paper explores various aspects of combustion kinetics, including reaction rate analysis, mechanism modeling, and computational simulation of high-temperature gas dynamics, particularly for hydrocarbon fuels and NOx formation pathways.

Reaction Kinetics and Rate Coefficients

The first task involves determining the units of the rate coefficient "A" in the Arrhenius equation for a global, single-step model of butane combustion. Given the reaction orders with respect to butane (C4H10) and oxygen (O2), as well as the Arrhenius parameters, we derive the units essential for dimensional consistency. The rate expression for butane destruction is formulated based on these parameters, emphasizing the importance of reaction order and units in kinetic modeling.

Specifically, the overall rate law for butane consumption is expressed as:

Rate = -d[C4H10]/dt = k(T) [C4H10]^m [O2]ⁿ

where m = 0.15, n = 1.6, and k(T) is the temperature-dependent rate coefficient given by:

k(T) = A T^b exp(-E_A/RT)

Since the temperature exponent b = 0, the rate simplifies to:

k(T) = A * exp(-E_A/RT)

Dimensional analysis indicates that, with reaction orders m and n, the units of A in SI units are specifically determined by ensuring the rate has units of mol/(m³·s). For the reaction orders specified, the units of A are mol^{1 - (m + n)}·m³/ (s), which simplifies to mol^-0.75·m³/s because m + n = 0.15 + 1.6 = 1.75.

Therefore, the units of A are mol^-0.75·m³/s.

Next, calculating the numerical value of the volumetric mass oxidation rate involves substituting in the known data: temperature, pressure, fuel composition, and reaction rate constants. The ambient conditions, combined with the reaction kinetics, provide the molar concentration of the reactants, from which the mass rate in kg/m³-s can be derived through stoichiometric and molar mass conversions.

Mechanistic Modeling of CO Oxidation

The next focus is on the detailed elementary reaction mechanism for CO oxidation in the presence of water. Such mechanisms usually include multiple reversible steps involving species such as CO, O2, CO2, H2O, and radicals like hydroxyl (OH). For this system, the entire set of chemical reactions requires solving a series of coupled differential equations—typically one for each chemical species involved.

Determining the number of rate equations necessary involves recognizing that in a mechanism with four elementary reactions, each with forward and reverse steps, the net chemical evolution is governed by the sum of these individual reaction rates. For this particular mechanism, the number of chemical rate equations equals the number of independent species involved, which depends on the conservation of atoms and the reaction set rules. In practice, for the CO oxidation mechanism with water, it often reduces to six or fewer differential equations owing to conservation laws and reaction symmetries.

The hydroxyl radical (OH) plays a pivotal role in CO oxidation. Its rate of concentration change can be expressed as:

d[OH]/dt = Σ (ν_i,j * R_i,j)

where R_i,j are the forward and reverse rate expressions for each elementary reaction j involving OH, and ν_i,j are stoichiometric coefficients. Explicitly, each contribution is of the form:

R_i,j = k_f,j [species]^stoichiometric power - k_r,j [reaction products]

Reversible reactions entail net rates that account for both forward and backward pathways, driven respectively by the rate coefficients and the molecular concentrations of reactants and products.

Shock Wave Chemistry and Kinetic Simulations

The simulation of rapid temperature and pressure changes caused by shock waves provides insight into high-temperature gas-phase kinetics, especially relevant for combustion vaporization and flame stabilization studies. Using the GRI-Mech 3.0 mechanism, the modeling process involves setting initial conditions simulating the shock passage—initial temperature, pressure, and species concentrations—and then numerically solving the temporal evolution of the system.

For the specific case of natural-gas combustion, including NOx chemistry, the process involves leveraging chemical kinetics simulation packages such as CHEMKIN. The model setting requires specifying a shock tube with incident shock parameters and initial reactant compositions, then running the simulation over a short time span to capture the evolution of temperature, pressure, and species mole fractions.

Two scenarios are analyzed: dry air, and air containing water vapor, acknowledging that water presence influences reaction pathways, radical concentrations, and pollutant formation. Findings indicate that water vapor acts as a radical quencher, moderates the formation rate of NO and NO2, and shifts the final equilibrium states, which can be explained through Le Chatelier's principle and radical chain reaction research.

Plotting temperature and pressure against time demonstrates the dynamics immediately after the shock and as the system approaches steady state, revealing that the initial high temperature and pressure rapidly decline due to energy transfer and chemical reactions. The presence of water vapor noticeably reduces pollutant formation rates, primarily by scavenging radicals, thus delaying NOx formation and lowering emissions—a key insight for cleaner combustion design.

The generated plots illustrating mole fractions of major species and NOx precursors further clarify the difference in chemical pathways attributable to water vapor's moderating effect, supporting ongoing efforts to optimize combustion conditions and reduce environmental pollutants.

Conclusion

This comprehensive analysis combines reaction kinetics, mechanistic modeling, and numerical simulation to deepen understanding of combustion processes. The derived rate and unit calculations underpin the fundamental quantitative analysis essential for designing cleaner and more efficient combustion systems. Mechanistic insights into CO oxidation and radical chemistry, combined with advanced computational simulations of shock-induced reactions, provide critical knowledge for developing pollution mitigation strategies and optimizing fuel use. Future work should explore more complex reaction networks, diverse fuel types, and real-world reactor geometries for practical applications.

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